two small objects, A and B, are fixed in place and separated by 3.00 cm in a vacuum. object A has a charge of +2.00 micro coulomb , and object B has a charge of -2.00 micro coulomb. how many electrons must be removed from A and put onto B to make the elecrtostatic force that acts on each object an attractive force whose magnitude is 68.0 N?
F=(1/4pii*8.85419*10^-12F/m)*Q1Q2/r^2
Since the charges were same just opposite you can put Q1Q2 as Q^2.
Solve Q.
Then deduct from the ansver the charge there already is and divide by elementary charge.
To calculate the number of electrons that need to be transferred between objects A and B, we need to use the formula that relates the electrostatic force and the charge:
F = k * |q1 * q2| / r^2
Where:
- F is the electrostatic force
- k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2)
- |q1 * q2| is the magnitude of the product of the charges of the objects
- r is the distance between the objects
In this case, we have F = 68.0 N, q1 = +2.00 μC, q2 = -2.00 μC, and r = 3.00 cm = 0.03 m.
First, we can calculate the magnitude of the product of the charges:
|q1 * q2| = |(+2.00 μC) * (-2.00 μC)|
= |2.00 μC * 2.00 μC|
= 4.00 μC^2
Now, let's plug in the known values into the formula:
68.0 N = (8.99 x 10^9 N m^2/C^2) * (4.00 x 10^-12 C^2) / (0.03 m)^2
To solve for the number of electrons transferred, we need to convert the charge from coulombs to elementary charges (electron charge).
1 coulomb = 6.24 x 10^18 elementary charges
So, 4.00 x 10^-12 C = (4.00 x 10^-12 C) * (6.24 x 10^18 elementary charges / 1 C)
Now, we can substitute the converted charge into the formula and solve for the number of electrons:
68.0 N = (8.99 x 10^9 N m^2/C^2) * [(4.00 x 10^-12 C) * (6.24 x 10^18 elementary charges / 1 C)] / (0.03 m)^2
Simplifying the equation and solving for the number of electrons:
Number of electrons = [(68.0 N) * (0.03 m)^2] / [(8.99 x 10^9 N m^2/C^2) * (4.00 x 10^-12 C) * (6.24 x 10^18 elementary charges / 1 C)]
By performing the above calculation, we can determine the number of electrons that need to be removed from object A and put onto object B.